Mathematical Research Letters

Volume 15 (2008)

Number 2

Totally geodesic subgraphs of the pants complex

Pages: 309 – 320



Javier Aramayona (University of Warwick)

Hugo Parlier (Ecole Polytechnique Fédérale de Lausanne)

Kenneth J. Shackleton (T. I. Tech.)


In recent work of Brock's, the pants graph is shown to be a combinatorial model for the completion of the Weil-Petersson metric on Teichmüller space. We prove that every Farey graph embedded in the pants graph is totally geodesic, in analogy with the extrinsic geometry of any $2$-dimensional stratum inside the Weil-Petersson completion.

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